Validation of a Control Algorithm for Human-like Reaching
Motion using 7-DOF Arm and 19-DOF Hand-Arm Systems
Tapomayukh Bhattacharjee, Yonghwan Oh* and Sang-Rok Oh
Abstract— This technical report gives an overview of our
work on control algorithms dealing with redundant robot
systems for achieving human-like motion characteristics. Pre-
viously, we developed a novel control law to exhibit human-
motion characteristics in redundant robot arm systems as
well as arm-trunk systems for reaching tasks [1], [2]. This
newly developed method nullifies the need for the computation
of pseudo-inverse of Jacobian while the formulation and
optimization of any artificial performance index is not neces-
sary. The time-varying properties of the muscle stiffness and
damping as well as the low-pass filter characteristics of human
muscles have been modeled by the proposed control law to
generate human-motion characteristics for reaching motion
like quasi-straight line trajectory of the end-effector and
symmetric bell shaped velocity profile. This report focuses on
the experiments performed using a 7-DOF redundant robot-
arm system which proved the effectiveness of this algorithm in
imitating human-like motion characteristics. In addition, we
extended this algorithm to a 19-DOF Hand-Arm System for
a reach-to-grasp task. Simulations using the 19-DOF Hand-
Arm System show the effectiveness of the proposed scheme for
effective human-like hand-arm coordination in reach-to-grasp
tasks for pinch and envelope grasps on objects of different
shapes such as a box, a cylinder, and a sphere.
I. INTRODUCTION
Robots have increasingly been used in human environ-
ments for dexterous manipulation. Redundancy is almost
a prerequisite in such cases because it can be used to
manipulate or reach objects in human environments dex-
terously. Control of such redundant humanoid arm systems
for reaching motion should achieve human-motion charac-
teristics like quasi-straight line trajectory of human arm and
bell-shaped tangential velocity profile for their acceptability
in human society [1], [2]. The authors, in their previous
work in [1], [2] have developed a control algorithm which
can imitate the common human-motion characteristics for
redundant arm as well as arm-trunk systems. The new con-
trol scheme successfully demonstrates both quasi-straight
line end-point trajectory and symmetric bell-shaped velocity
profile as well as the temporal characteristics of such arm-
trunk motion [1], [2].
In this short report, we validate the theory using real-time
experimental results using a 7-DOF Robotic Arm system
which prove the efficacy of this algorithm in presence of
During this work, T. Bhattacharjee was with the Interaction and Robotics
Research Center, KIST, 39-1 Hawolgok-dong, Wolsong Gil 5, Seongbuk-
gu, Seoul 136-791, South-Korea. Now, he is with Georgia Institute of
Technology, USA
Y. Oh, and S. R. Oh are with the Interaction and Robotics Research
Center, KIST, 39-1 Hawolgok-dong, Wolsong Gil 5, Seongbuk-gu, Seoul
136-791, South-Korea {oyh, sroh}@kist.re.kr
*Y. Oh is the corresponding author
non-linear uncertainties. We also extend this algorithm to
multiple-DOF Hand-Arm systems for Reach-to-Grasp tasks.
We test this extended formulation using a 19-DOF Robotic
Hand-Arm System in a real-time simulation software en-
vironment called RoboticsLab for various Reach-to-Grasp
tasks which involve grasping objects of different shapes
such as a box, a cylinder, and a sphere using pinch and
envelope grasps.
The rest of the report is organized as follows. At first,
we provide an overview of our previously developed control
law based on [1], [2] in Section II. We then describe our
experimental setup for the 7-DOF Arm system in Section
III. Section IV describes the experimental results in detail.
Our extended control algorithm for hand-arm coordination
in reach-to-grasp tasks is presented in Section V. Section VI
describes the results of the extended algorithm for different
reach-to-grasp tasks using objects of different shapes with
pinch and envelope grasps. The links to the videos of the
above experimental and simulation results are provided in
the respective sections. Section VII concludes the report.
II. HUMAN MOTION CHARACTERICTICS
Human motion occurs as a result of various muscle move-
ments, their coordination and the brain muscle communi-
cation. For reaching or pointing movements, the primary
human motion characteristics which have been identified
were the quasi-straight line trajectory of the arm and
symmetric bell shaped velocity profile as given in [6],
[7]. However, for reaching movements involving the trunk,
additionally researchers have identified some more temporal
characteristics such as the peak velocity of the trunk occurs
after the peak velocity of the arm which can also be
noticed from [7], [8]. Also, it was noticed that the trunk
starts moving with or before the arm by around 10 ms but
continues to move even after the arm motion has ceased for
around 100 −200 ms more [7], [8].
Though there have been many works speculating about
the probable causes of such characteristics, there have
not been any conclusions and till date the mechanism by
which the nervous system controls the redundant degrees-
of-freedom to accomplish a task is far from being under-
stood [4]. However, researchers have claimed that human
muscles can be modeled using a spring and a damper with
time-varying characteristics [9]. It is argued that muscle
stiffness drops during movement while muscle damping
increases in motion and the variation of these dynamics
are in a sinusoidal manner [9], [10]. Also, they are joint-
dependent and non-linear in nature [10]. Hence, there is a
arXiv:1311.0959v1  [cs.RO]  5 Nov 2013
need for a time-varying, non-linear, joint-dependent model
for muscle stiffness and damping. Although, Arimoto et.
al. have claimed to improve the velocity profile by using
a time-varying stiffness model [5], the results were not
satisfactory probably because their time-varying model had
a sudden and drastic increase in the beginning of the motion
and then remained constant thereafter which is unlike the
actual behavior noticed [10]. Also, the model in [5] is
developed based on an assumption that the actin-myosin
interactions which generate the force could be assumed to
be a stochastic process and hence, a gamma distribution had
been applied. This assumption had no strong evidence. In
addition to the above, it has also been identified that human
muscles have low-pass filter characteristics and there is a
slight delay in brain to muscle communication due to the
nervous system path ways which affects the motion pattern
[11], [12], [13]. A joint dependent low-pass filter is, there-
fore, needed to exhibit the low-pass filter characteristics of
human muscles. Also, low-pass filters generate an amount
of delay which can account for the delay in brain to muscle
communication in humans. The proposed control algorithm
has been developed based on these needs identified.
A new control law has thus been developed based on
the needs identified for characterizing the human motion
features in reaching movements involving the trunk. The
control law is given below in (1).
u = −Wf
h
KV ˙q + kFmus JT (q)∆x
i
,
(1)
where joint damping matrix KV is given by
KV = diag
h
C∗
1(t) C∗
2(t) C∗
3(t) C∗
4(t) C∗
5(t) C∗
6(t) C∗
7(t)
i
(2)
and
C∗
i (t) = Ci sin (π (∥∆x0∥−∥∆x∥) /2 ∥∆x0∥) .
(3)
k is the virtual spring and Fmus is a bijective joint muscle
mapping function given by
Fmus = diag
h
f ∗
1 (t) f ∗
2 (t) f ∗
3 (t) f ∗
4 (t) f ∗
5 (t) f ∗
6 (t) f ∗
7 (t)
i
(4)
and
f ∗
i (t) = fi cos (π (∥∆x0∥−∥∆x∥) /2 ∥∆x0∥) ,
(5)
where fi denotes the joint muscle stiffness coefficient and
Wf = diag

1
τis + 1

,
for i = 1, . . . , 7 .
(6)
As given in the control law shown in (1), the control input
to the joint actuators is a function of a damping shaping
term given by KV and a bijective joint muscle mapping
function given by Fmus.
The damping shaping term KV
is assumed to be a
diagonal matrix whose elements are time-varying functions.
This matrix shapes the control input based on the joint
actuator velocities and is taken to be diagonal by assuming,
without any loss of generality, that velocity coupling is
negligible between the different joints. Each of the diagonal
elements is modeled by a sinusoidal function based on the
current distance of the end-effector with that of the target
point. As shown in (3), ∥∆x0∥represents the two-norm
of the initial distance of the end-effector with that of the
target point while ∥∆x∥represents the current distance of
the end-effector with that of the target point and is updated
at every time-instant. The sinusoidal function is so chosen
such that the damping shaping term vanishes at the start
of the motion as ∥∆x∥→∥∆x0∥, and then gradually
increases during motion till it reaches a maximum value.
This time-varying nature is modeled in accordance with the
trend noticed for muscle damping in reaching movements
[10]. The weighting factors Ci are tuned for appropriate
trajectory and velocity characteristics where i = 1, . . . , 7.
The Fmus function on the other hand, is modeled as
a time-varying joint dependent bijective muscle mapping
function. It is bijective because for every joint actuator
there is a unique corresponding one-to-one mapping to a
time-varying weighting variable which forms the diagonal
elements of the function matrix whose dimension is given
by the number of degrees of freedom of the robot. This
function, as shown in (4), acts on the virtual work done
to reach the target. A virtual spring is attached to the end-
effector which literally pulls the robot end-effector towards
the target point where k denotes the stiffness of the virtual
spring. The spring force generates a virtual work which is
required to be done by the joint actuators to move the robot
to that desired target position and is given by kJT (q)∆x.
This mechanical work is then mapped to appropriate joint
muscle stiffness values by the mapping function given in
(4). The time-varying nature of each element is modeled by
a cosine function based on the current distance of the end-
effector with that of the target point. As shown in (5), the
cosine function is so chosen such that the muscle stiffness
value is maximum before the motion starts as ∥∆x∥→
∥∆x0∥, and then gradually decreases during motion. This
time-varying nature is modeled in accordance with the
trend noticed for muscle stiffness in reaching movements
[10]. The joint muscle stiffness coefficients fi are tuned
for appropriate trajectory and velocity characteristics where
i = 1, . . . , 7.
This control action is then processed by a low-pass
filter matrix, as shown in (6), because muscles exhibit
inherent low-pass filter characteristics [11], [12], [13]. The
dimension of the matrix corresponds to the number of
the degrees of freedom of the robot and each element is
modeled as a first-order low pass filter as shown in (6)
whose time-constant τi is tuned for appropriate behavior.
This low-pass filter also introduces a delay between the
control input and the joint actuator torque output which
functions as the brain-muscle communication delay existing
in humans and hence, the time-constant of these joint-
dependent filters are important factors in the design of the
control law. The resultant control block diagram is shown
in Fig. 1.
Fig. 1.
Block diagram representation of the control law.
Fig. 2.
Experimental Setup of a 7-DOF Redundant Robot Arm.
III. EXPERIMENTAL SETUP
To judge the effectiveness of the proposed algorithm, we
conducted experiments using a newly built 7-DOF Robot
Arm. The experimental setup is as shown in Fig. 2.
The first 4 joints are driven by Kollmorgen Motors while
the last 3 are driven by Maxon motors. They are connected
to the PC through Elmo Digital servo drives and encoders
are attached to each of these motors. CANOpen protocol
has been used for communication purposes.
Before, we use this 7-DOF robot arm as a platform to
verify our developed control law, we need to cancel the
undesired dynamic effects and nonlinear uncertainties of
this platform. We implemented a Task-Space Disturbance
Observer, as given in [3], to cancel the disturbance terms.
For this purpose, we need to compute the Inertia, Coriolis,
Gravity, and Friction Terms for compensating the undesired
dynamic effects as shown in Section III-A.
A. Dynamic Formulation of Inertial, Coriolis, Gravity, and
Friction Forces
The computation of the dynamic forces like Inertial,
Coriolis, Gravity and Friction forces for a 7-DOF redundant
robot is not a trivial task and is computationally very ex-
pensive. Hence, we employ the modified recursive Newton-
Euler Algorithm for computing these forces [9]. Based on
[9], our recursive algorithm denoted as NE∗
α(q, ˙q, ˙qa, ¨q) is
given as follows:
ωi = ωi−1 + ˙qizi−1
(7)
ωai = ωai−1 + ˙qaizi−1
(8)
˙ωi = ˙ωi−1 + ¨qizi−1 + ¨qiωai−1 × zi−1
(9)
¨Oi = ¨Oi−1 + ˙ωi × ri−1,i + ωi × (ωai × ri−1,i)
(10)
¨Bi = ¨Oi + ˙ωi × ri,Bi + ωi × (ωai × ri,Bi)
(11)
fi = fi+1 + mi ¨Bi
(12)
τi = τi+1 −fi × (ri−1,i + ri,Bi) + fi+1 × ri,Bi
+Ii ˙ωi + ωai × (Iiωi)
(13)
ui = τ T
i zi−1
(14)
where ωi denotes the angular velocity of link i, qi is the
angle of joint i and their derivatives have usual meanings,
zi is the unit vector in the direction of velocity of joint i,
Oi is the origin of the i-th reference frame, Bi is the origin
of the center of mass of link i, fi and τi are the force and
torque acting on link i, ˙qai is the auxiliary velocity of joint
i, ri−1,i = Oi −Oi−1, and ri,Bi = Bi −Oi.
Therefore, the joint-space Inertial, Coriolis, and Gravity
terms are derived as follows.
Mij(q) =
⌢v
T
i NE∗
α(q, 0, 0,
⌢v j)
(15)
C∗
ij(q, ˙q) =
⌢v
T
i NE∗
α(q, ˙q,
⌢v j, 0)
(16)
G∗
i (q) =
⌢v
T
i NE∗
α(q, 0, 0, 0, g)
(17)
where i, j can be taken from 1 to the number of joints
and
⌢v j denote a column vector with 1 as the j-th term and
0 as all other terms. g is the acceleration due to gravity and
its magnitude is 9.81m/s2.
The Friction term is calculated as,
fri (q) = η ˙q + µ tanh(β ˙q)
(18)
where fri is the joint frictional force, η is the coefficient
of viscous friction and µ is the coefficient of coulomb
friction.
B. Computation of the Time-Derivative of Jacobian
The Inertial and Coriolis terms, derived in Section III-
A, are joint-space based terms. To convert it to the task-
space based formulation so that these can be applied in
our task-space disturbance observer, we use the formulation
given in [3]. However, we might note that the derivative
of the Jacobian needs to be computed to perform this
transformation, which is not easy. Here, we explain the
manner in which the time-derivative of the Jacobian has
been computed for this work.
If the Jacobian can be denoted as given below,
J =

ei
pi × ei

(19)
then,
˙J =

˙ei
∂
∂t (pi × ei)

=

˙ei
˙pi × ei + pi × ˙ei

(20)
where
˙ei = ωi × ei with ωi =
i−1
X
j=1
˙qjej
˙pi =
j−1
X
k=i
˙pk,k+1 with ˙pk,k+1 = ωk × pk,k+1
(21)
Thus, the time-derivative of the Jacobian can be com-
puted.
IV. EXPERIMENTAL RESULTS
After the undesired dynamic effects for the 7-DOF Robot
Arm were compensated, we implemented the control algo-
rithm as given in Section II. Let Ii denote the inertia tensors
for all the links of the robot wherein i = 1, . . . , 7 and the
diagonal elements are given by Ixx, Iyy, and Izz which
are the principal moments of inertia. The non-diagonal
elements given by Ixy, Iyz, and Ixz are negligible for
highly symmetric construction of links. Let ℓi, COM, and
mi denote the link lengths, distance of Center of Masses
of links from link frames and link masses respectively. The
lengths of the links as well as the dynamic parameters such
as the link inertia and mass properties are based on manu-
facturer specifications and rough human measurements, and
are given in Table I. The calculated coulomb and viscous
friction coefficients of every joint are also given in Table I.
All dimensions used in this report are in S.I. units.
Using the above parameters and the mathematical for-
mulation as described in Section III-A, we compen-
sated for the undesired dynamic effects including fric-
tion and gravity effects. β for friction compensation
was taken as 20. A video, which shows the results
TABLE I
ROBOT PARAMETERS
Joint
Joint
Joint
Joint
Joint
Joint
Joint
1
2
3
4
5
6
7
Ixx
0.006
0.012
0.003
0.005
0.001
0.002
0.001
Iyy
0.001
0.002
0.000
0.001
0.000
0.001
0.000
Izz
0.006
0.011
0.003
0.005
0.001
0.002
0.001
ℓ
0.085
0.171
0.069
0.148
0.095
0.0
0.0755
COM
0.011
0.091
0.007
0.051
0.058
0.0
0.0185
m
0.81
2.096
0.538
0.407
0.459
0.396
0.135
µ
3.704
5.02
1.359
1.240
0.607
0.979
0.778
η
1.104
2.086
1.191
1.016
0.668
0.794
0.604
TABLE II
CONTROL PARAMETERS
Joint
Joint
Joint
Joint
Joint
Joint
Joint
1
2
3
4
5
6
7
Ci
20
10
20
10
10
10
0.1
fi
180
40
10
20
1
1
1
τi
0.015
0.015
0.015
0.015
0.015
0.015
0.015
of our friction and gravity compensation methods, is
uploaded in https://docs.google.com/leaf?id=
0B5IkR-5za8vGanFSMkFwWnJhWHM. After compen-
sating the undesired dynamics, we implement the developed
control law in the 7-DOF robot arm. For implementing the
algorithm according to Section II, we have selected the
parameters as given in Table II. The spring constant of the
virtual spring is taken as k = 13 N/m and the target position
was given at Xd = 0.3m, Yd = 0.3m, and Zd = −0.3m.
The initial position of the robot is at X0 = 0.085m, Y0 =
0.0m, and Z0 = −0.5585m.
The results of the experiments are given below in Figs.
3 and 4 and these results show that the proposed algo-
rithm successfully imitates human-motion characteristics
for multi-DOF redundant robotic arm systems for reaching
tasks.
The
experimental
video
which
shows
the
overall
performance
of
the
7-DOF
Robot
Arm
in
reach-
ing
to
a
particular
goal
with
compliance
is
up-
Fig. 3.
Quasi-Straight Line Trajectory for Reaching Tasks in Non-Gravity
Plane.
Fig. 4.
Bell Shaped Velocity Profile for Reaching Tasks.
loaded in https://docs.google.com/leaf?id=
0B5IkR-5za8vGVTlsR2dFWEdIQ2s.
V. EXTENDED HAND-ARM CONTROL LAW
We extended the Arm Control Law to a 19-DOF Hand-
Arm System to see if the Extended/Unified Hand-Arm
Control law can be used for reach-to-grasp tasks. The
extension is straight-forward such that it is equivalent to
adding 4 serial 3-DOF arms (or fingers) to the 7-DOF
robotic arm. However, the main challenge lies in the fact
that there is a huge difference in the mechanical parameters
such as inertia between the bulky arm and the light fingers
and hand. Hence, to cancel the effect of coupling that might
effect the finger movements due to the inertia and other
dynamic effects of the arm, we employed a joint-space
disturbance observer. The entire 19-DOF Hand-Arm system
is shown in Fig. 5. The Unified Hand-Arm Control Law is
shown in Fig. 6.
VI. HAND-ARM COORDINATION: SIMULATION
RESULTS
Simulations using the real-time simulation software en-
vironment called RoboticsLab were performed for various
Reach-to-Grasp tasks which involve grasping objects of
different shapes such as a box, a cylinder, and a sphere
using pinch and envelope grasps. Simulation results show
the efficacy of the Unified Hand-Arm Control law for such
reach-to-grasp tasks for all the above objects and grasp
types. The results are shown in Fig. 7.
The
resulting
simulation
video
of
all
the
above
grasps
for
all
the
three
different
objects
is
up-
loaded in https://docs.google.com/leaf?id=
0B5IkR-5za8vGZ1N3bkhsTFN3MTQ.
VII. CONCLUSION
In this report, we presented a novel control algorithm to
exhibit the spatial and temporal characteristics of human
reaching movements for multi-DOF robot arm systems
based on our previous results. The newly developed control
algorithm is developed based on the observed human muscle
stiffness and damping properties. This control scheme takes
into account the time-varying, joint dependent character-
istics of the muscle stiffness and damping as well as
Fig. 5.
A Robotic Hand-Arm System with 7-DOF Arm and 12-DOF
Hand.
Fig. 7. Sequence of steps of a 19-DOF robotic Hand-Arm System grasping
three objects using the Unified Hand-Arm Law : Top: Box with Pinch
Grasp, Middle: Cylinder with Envelope Grasp, and Bottom: Sphere with
Pinch Grasp.
Fig. 6.
A Block Diagram Representation of the Unified Hand-Arm Control Law for a 7-DOF Arm and 12-DOF Hand using Joint-Space Disturbance
Observers.
the low-pass filter characteristics of human muscles and
also considers the communication delay in brain-muscle
communication. We implemented this control algorithm
using a 7-DOF Robotic Arm and the experimental results
also show the effectiveness of this algorithm in describing
the characteristics of the human reaching motion. We com-
pensated the friction and gravity effects and canceled the
undesirable dynamic effects using a Task-Space disturbance
Observer. We extended this algorithm to a Unified Hand-
Arm Control Law for effective Hand-Arm Coordination
in reach-to-grasp tasks. Simulations were conducted using
a 19-DOF Hand-Arm system for reaching and grasping
objects of different shapes such as a box, a cylinder and
a sphere using pinch and envelope grasps. We implemented
a joint-space disturbance observer to cancel the coupling
effects between the bulky arm with high inertia and the
light-weight fingers. Results show the effectiveness of the
Unified Hand-Arm Control law for Hand-Arm Coordination
in such reach-to-grasp tasks.
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